CAREER: Quantum Entanglement and Geometric Frustration in Correlated Metals

University Of California-San Diego, La Jolla CA

Investigators

Abstract

NONTECHNICAL SUMMARY This CAREER supports research and education on long-standing conceptual questions in the quantum condensed matter physics of metallic systems. Most materials order in one pattern or another as the temperature decreases. For example, water molecules order to form ice crystals at low temperatures. However, there exists an interesting possibility whereby a material doesn't order even at the absolute zero temperature; such materials go by the moniker "quantum liquids". One of the major theoretical discoveries of the past decade is that quantum liquids are distinguished by a feature of exclusively quantum nature: they are highly entangled objects. In an entangled quantum system, the state of an individual component cannot be described independently of the other components. In a quantum liquid, approximately a trillion trillion particles can be entangled with each other! Due to its counter-intuitive properties, quantum entanglement potentially offers exciting applications ranging from ultrafast computing to novel encryption schemes. At the same time, however, entanglement can often be fragile. Therefore, a key question is: where to look for materials with robust entanglement? The PI and his group will develop a multipronged approach to study highly entangled materials by combining tools from theoretical physics, quantum information science, and state-of-the-art computational algorithms. Developing proper understanding will allow the researchers to make precise predictions, which is essential for harnessing the technological potential of quantum entanglement. Another desired goal is to develop a deeper understanding of strongly interacting matter using ideas from computer science. Such progress will potentially impact several areas of scientific inquiry at once, ranging from quantum materials to high-energy particle physics and quantum information science. The algorithms and software developed will be disseminated to the community in open-source form. In tandem with the research project, the PI will organize and participate in a variety of educational and outreach activities. Firstly, the PI will try to bring the excitement of quantum physics to undergraduates by presenting introductory lectures on the PI's research. Secondly, the PI will organize a yearly workshop aimed at socio-economically disadvantaged high-school students, which will develop skills in formulating estimates relevant for everyday life. Finally, the PI will mentor undergraduate and graduate students on research topics closely aligned with the research component. TECHNICAL SUMMARY This CAREER supports research and education on long-standing conceptual questions in the quantum condensed matter physics of metallic systems. Specifically, the PI will focus on questions informed by materials which either do not fit within Landau's Fermi liquid theory, or whose description solely in terms of conventional symmetry-breaking order parameters misses key physical aspects. A common thread connecting these materials is that they are highly quantum entangled. To make progress, the PI will develop new ideas and tools at the intersection of quantum information theory, quantum field theory and state-of-the-art Quantum Monte Carlo (QMC) techniques. One of the big impediments in understanding strongly correlated metals is the Fermion sign problem. The problem is compounded when the fermions are further coupled to geometrically frustrated spins. Such a set-up is directly relevant for a wide variety of frustrated heavy-fermion systems. To make progress on this front, the PI will implement a newly discovered algorithm that for the first time allows for unbiased simulations of a large class of frustrated Kondo lattice systems. This approach will also shed light on the entanglement structure of frustrated metallic systems. The PI will also study the global phase diagram of heavy fermions from a quantum-information-theoretic perspective. The expected outcomes of this research are: 1) Predictive power on a large class of Hamiltonians that model correlated metals potentially relevant for quantum technologies. 2) A quantum-information-theoretic understanding of the global phase diagram of correlated metals. 3) Development of new computational algorithms that will be capable of addressing a wide range of problems relevant to distinct areas of quantum physics, from condensed matter physics to atomic physics and high-energy particle physics. The algorithms and software developed will be disseminated to the community in open-source form. In tandem with the research project, the PI will organize and participate in a variety of educational and outreach activities. Firstly, the PI will try to bring the excitement of quantum physics to undergraduates by presenting introductory lectures on the PI's research. Secondly, the PI will organize a yearly workshop aimed at socio-economically disadvantaged high-school students, which will develop the skill of using order-of-magnitude estimates relevant for everyday life. Finally, the PI will mentor undergraduate and graduate students on research topics closely aligned with the research component. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.